I am not being facaetious with this answer - Im not going to say things like a personal apperation because we understand a lot about hallucinations so Im not even sure that would convince me BUT things that would make me sit up and take notice would be:
Answering Prayers - as per the numerous and unconditional claims for this in the Bible - but not on an individual basis, on a mass, consistent, universal basis.
Healing - Jesus tells the disciples, and presumably his priests, their descendants, to heal the sick, cure the lame, raise the dead. For priests to evidence not just a spiritual healing ministry, but a physical one, where we can study those healed - that would include amputee limb regeneration, obliteration of all cancers, etc.
Unity - all christian sects (Im leaving out the myriad of other different religions for now) claim to have the Holy Spirit as their guide. Yet they all disagree with one another on some level - some superficial some so profound they condemn other christian sects and claim they are not even christian - this to me is evidence there is no Holy Spirit guiding but rather mans mind and personal interpretation - so let’s see total and absolute unity of christian belief, one single church, one single set of beliefs, all arrived at independently by different people of different cultures and different languages and all completely agreeing with each other on every single level.
Visionaries - I have never been able to understand why visionaries almost always seem to be devout, humble, simple, often uneducated and very young, people - who then give messages to Bishops or the Pope and in the case of Fatima, keep things secret for decades.
Appear at the next Atheist Conference, or the United Nations - and not invisibly, visibly, so there is no ambiguity or personal interpretation involved - with a clear unambiguous message.
Christian behavior - I know and have dealings with some wonderful christian people. They do, it seems to me, try to live out their faith day by day. But the vast majority of people I know and deal with, while saying theyre christian, just go about their daily business, and it seems, that although they believe they have access to some wonderful news or secret about salvation and believe, genuinely, they are going to, or have a good chance of getting to, heaven, where they will live for all eternity, it doesnt seem to make the slightest bit of difference to them on just about any level.
They are moody, rude, miserable, greedy, selfish, covetous, thieving, lying, adulterating, cheating, deceiving, blaspheming and occasionally murderous.
Finding a rabbit in the precambrian fossil record
That would do for starters. It would certainly give me something to think about and wonder why that should be so.